Bi-local baryon interpolating fields with two flavors
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We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transformation properties of these fields and place them into baryon chiral multiplets. Thus we derive the independent baryon interpolating fields with given values of spin (Lorentz group representation), chiral symmetry (U L (2)×U R (2) group representation) and isospin appropriate for the first angular excited states of the nucleon.
KeywordsChiral Multiplet Pauli Principle Fierz Identity Chiral Transformation Axial Transformation
- 16.H.X. Chen, V. Dmitrasinovic, A. Hosaka, arXiv:1009.2422 [hep-ph]